Abstract

The pseudodifferential operator (p.d.o.) A(x,D), associated with the Bessel operator d2/dx2+(1−4μ2)/4x2, is defined. Symbol class Hρ,δm is introduced. It is shown that the p.d.o. associated with a symbol belonging to this class is a continuous linear mapping of the Zemanian space Hμ into itself. An integral representation of p.d.o. is obtained. Using Hankel convolution Lσ,αp-norm continuity of the p.d.o. is proved.

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